Download - Vectors and Scalars Physics
Vectors and Scalars
Physics
Bell Ringer 10/13/15 Answer the following on your bell ringer
sheet:
1. Is displacement a vector or scalar? 2. What is the difference between vectors & scalars?
NB: Don’t forget to write your objective in your notebook before we start.
Scalar
A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.
Magnitude – A numerical value
Scalar Example
Magnitude
Speed 20 m/s
Distance 10 m
Age 15 years
Heat 1000 calories
Vector
A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION.
Vector Magnitude & Direction
Velocity 20 m/s, N
Acceleration 10 m/s/s, E
Force 5 N, West
Faxv ,,,
Objective
We will use a treasure hunt activity to create a vector addition map
I will map the course taken and add vectors to find the resultant.
3F “ graphical vector addition”
Agenda
Cornell Notes- Essential Questions Vector treasure hunt Vector Map
Cornell Notes Essential Questions:
What is a vector? How do we represent vectors? How do we draw a vector?
What shows the magnitude? What shows the direction?
When should vectors be added? When should vectors be subtracted? What is the resultant vector?
Vectors
Vectors Quantities can be represented with;
1. Arrows2. Signs (+ or -) 1-D motion3. Angles and Definite Directions
(North, South, East, West)
Vectors Every Vector
TailHead
Vectors are illustrated by drawing an ARROW above the symbol. The head of the arrow is used to show the direction and size of the arrow shows the magnitude
Vector AdditionVECTOR ADDITION – If 2 similar vectors point in
the SAME direction, add them.
Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started?
54.5 m, E 30 m, E+
84.5 m, E
Vector Subtraction
VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT.
Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?
54.5 m, E
30 m, W-
24.5 m, E
Resultant
The vector representing the sum of two or more vectors is called the resultant vector.
Vector Treasure Hunt Create directions that lead to a specific
object/picture. You must have at least 4 turns. Generate a map from your origin ( door) to
your picture. Write each direction on an index card. Scramble the index cards and follow them
again. Then,( tomorrow) Create a vector map of total
displacement
CompassFront of
room
Back of room
Front door
Teacher Model
Directions to object with at least 4 turns from the front door.
Create a Map
Map drawn to scale.
ExampleYou walk 35 meters east then 20 meters north. You walk another 12 meters west
then 6 meters south. Calculate the Your displacement.
35 m, E
20 m, N
12 m, W
6 m, S
- =23 m, E
- =14 m, N
23 m, E
14 m, NR
Vector Map
Resulta
nt
25 ft South
50 ft
Ea
st
Expectation
Groups of 3-4 2 minutes to find the picture 10 minutes back track steps and create
directions on index cards 2 mins Shuffle cards Try to locate object from directions. 10 mins draw map to scale
Group Pictures
Group1- gorilla Group2- snake Group 3- rat Group 4- eagle Group 5- alligator Group 6- chicken Group 7- pig Group 8- dog
END
10/15/15 Bell Ringer ( 5 minutes!!) Get back to your
groups. 1.On large paper,
create a title, 2. Create a map of
your directions from origin to picture.
3. Create a Vector map by Summing up the vectors to find the horizontal and vertical components. Draw your resultant.
Write your names & turn in to teacher
ExampleYou walk 35 meters east then 20 meters north. You walk another 12 meters west
then 6 meters south. Calculate the Your displacement.
35 m, E
20 m, N
12 m, W
6 m, S
- =23 m, E
- =14 m, N
23 m, E
14 m, NR
Bell Ringer 10/15/15 4 minutes You walked 15 m east
from the door, then you walked 6 m south, then you turned around and walked back west 2 m, and another 6 meters west then you walked North 7 m.
Draw a vector diagram to show the motion and find the resultant.
Lesson objectives
We will use Pythagorean theorem to find the resultant, horizontal, and vertical components of vectors.
I will resolve a vector into its vertical and horizontal components and find the resultant using Pythagorean theorem.
Agenda Bell ringer Problems 1-4
Diagrams only Pythagorean theorem
( Solve for R) Grade papers Right angle triangles & Trig
functions
Note: You Need a calculator today & your notebook
Vector Addition Worksheet
Using Calculators Make sure it is in
degrees Locate the Sin, Cos,
& Tan buttons. Locate the 2nd button. Locate the Tan-1
Button.
Vectors
95 km,E
55 km, N
Start
Finish
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics
is called the RESULTANT.
Horizontal Component
Vertical Component kmc
c
bacbac
8.10912050
5595Resultant 22
22222
Vectors
95 km,E
55 km, N
Start
Finish
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics
is called the RESULTANT.
Horizontal Component
Vertical Component kmc
c
bacbac
8.10912050
5595Resultant 22
22222
Vectors
95 km,E
55 km, N
Start
Finish
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics
is called the RESULTANT.
Horizontal Component
Vertical Component kmc
c
bacbac
8.10912050
5595Resultant 22
22222
BUT……what about the direction?In the previous example, DISPLACEMENT was asked for
and since it is a VECTOR we should include a DIRECTION on our final answer.
NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE.
N
S
EW
N of E
E of N
S of W
W of S
N of W
W of N
S of E
E of S
N E
Bell Ringer 10/16/15 Its Friday!!!!! Check your grade in skyward. Write down
your current 2nd 6 weeks grade and your semester grade average.
Turn in Bell Ringer sheet.
Remember: Tests must be made up within a week of the test. Monday 10/19 is the deadline. Also late policy is in effect!
Agenda Review right angle triangle & Trig
functions ( SOH CAH TOA) How to enter Sin,Cos,Tan examples How to enter Sin-1,Cos-1, Tan-1
examples Example problems
How to find missing sides. How to find missing angles
Complete problems on your own
Note: You Need a calculator today
Lesson objectives
We will use trigonometry to find the missing side and the angles from right angle vector diagrams.
I will find the missing angle and missing side using trigonometry: Sine, Cosine, and Tangent functions.
Using Calculators Make sure it is in
degrees Locate the Sin, Cos,
& Tan buttons. Locate the 2nd button. Locate the Tan-1
Button.
Using Calculators Example 1: Use your
calculator to find the sin, cos, or tan or any angle.
Example 2: use your calculator to find the angle using the inverse ( Sin-1, Cos-1,& Tan-1)
Right angle triangle, 90Adjacent- Near the angle
Hypotenuse- the longest side
Opposite- opposite the angle
What if you are missing a side?
Which do I use?
What if you are missing a side?
Which will you use to find the missing sides? Pythagorean theorem or SOHCAH TOA?
Which do I use?
Trig triangles
What if you are looking for the angle? To find the value of the angle we use a Trig
function called the Inverse.
Which sides do we have?Which function do we use?
What if you are looking for the angle? To find the value of the angle we use a Trig
function called the Inverse.
What if you are looking for the angle?
Worksheet: Lesson 1
Reviewing the Primary Trigonometric ratios
Examples
What if you are missing a component?Suppose a person walked 65 m, 25 degrees East of North. What
were his horizontal and vertical components?
65 m25
H.C. = ?
V.C = ?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions since and cosine.
EmCHoppNmCVadj
hypopphypadjhypotenuse
sideoppositehypotenuse
sideadjacent
,47.2725sin65..,91.5825cos65..
sincos
sinecosine
SOH- CAH - TOA!!!!Let’s
identify the sides
What if you are missing a component?Suppose a person walked 65 m, 25 degrees East of North. What
were his horizontal and vertical components?
65 m25
H.C. = ?
V.C = ?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions since and cosine.
EmCHoppNmCVadj
hypopphypadjhypotenuse
sideoppositehypotenuse
sideadjacent
,47.2725sin65..,91.5825cos65..
sincos
sinecosine
SOH- CAH - TOA!!!!
What if you are missing a component?Suppose a person walked 65 m, 25 degrees East of North. What
were his horizontal and vertical components?
65 m25
H.C. = ?
V.C = ?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions since and cosine.
EmCHoppNmCVadj
hypopphypadjhypotenuse
sideoppositehypotenuse
sideadjacent
,47.2725sin65..,91.5825cos65..
sincos
sinecosine
BUT…..what about the VALUE of the angle???Just putting North of East on the answer is NOT specific enough
for the direction. We MUST find the VALUE of the angle.
N of E
55 km, N
95 km,E
To find the value of the angle we use a Trig function called the Inverse.
30)5789.0(
5789.09555
1
Tan
sideadjacentsideoppositeTan
109.8 km
So the COMPLETE final answer is : 109.8 km, 30 degrees North of East
BUT…..what about the VALUE of the angle???Just putting North of East on the answer is NOT specific enough
for the direction. We MUST find the VALUE of the angle.
N of E
55 km, N
95 km,E
To find the value of the angle we use a Trig function called the Inverse.
30)5789.0(
5789.09555
1
Tan
sideadjacentsideoppositeTan
109.8 km
109.8 km, 30 degrees North of East
BUT…..what about the VALUE of the angle???Just putting North of East on the answer is NOT specific enough
for the direction. We MUST find the VALUE of the angle.
N of E
55 km, N
95 km,E
.
30)5789.0(
5789.09555
1
Tan
sideadjacentsideoppositeTan
109.8 km
So the COMPLETE final answer is : 109.8 km, 30 degrees North of East
ExampleA bear, searching for food wanders 35 meters east then 20 meters north.
Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.
35 m, E
20 m, N
12 m, W
6 m, S
- =23 m, E
- =14 m, N
23 m, E
14 m, N
3.31)6087.0(
6087.2314
93.262314
1
22
Tan
Tan
mR
The Final Answer: 26.93 m, 31.3 degrees NORTH or EAST
R
ExampleA boat moves with a velocity of 15 m/s, N in a river which
flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.
15 m/s, N
8.0 m/s, W
Rv
1.28)5333.0(
5333.0158
/17158
1
22
Tan
Tan
smRv
The Final Answer : 17 m/s, @ 28.1 degrees West of North
ExampleA plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate
the plane's horizontal and vertical velocity components.
63.5 m/s
32
H.C. =?
V.C. = ?
SsmCVoppEsmCHadj
hypopphypadjhypotenuse
sideoppositehypotenuse
sideadjacent
,/64.3332sin5.63..,/85.5332cos5.63..
sincos
sinecosine
ExampleA storm system moves 5000 km due east, then shifts course at 40
degrees North of East for 1500 km. Calculate the storm's resultant displacement.
NkmCVoppEkmCHadj
hypopphypadjhypotenuse
sideoppositehypotenuse
sideadjacent
,2.96440sin1500..,1.114940cos1500..
sincos
sinecosine
5000 km, E
40
1500 km
H.C.
V.C.
5000 km + 1149.1 km = 6149.1 km
6149.1 km
964.2 kmR
91.8)364.0(
157.01.6149
2.96414.62242.9641.6149
1
22
Tan
Tan
kmR
The Final Answer: 6224.14 km @ 8.91 degrees, North of East
Hmm. That was good.
Holy Snakes!!!
It’s a bird, it’s a plane, It’s Super Rat!
Do I look like I’m playing?
Gator’s anyone?
Don’t be a chicken??
Do you think I’m cute? Yes or Nah? Yessss!!!!
What a time to be alive?